Place the apricot halves in a food processor and blend to a puree. Transfer the puree to a saucepan and bring to a simmer over low to medium heat. Add the sugar and the lemon juice and stir until the sugar dissolves and the puree thickens somewhat, about 10 minutes. Set aside to cool.
Whip the heavy cream until it holds soft peaks. To make the fool, fold the cooled apricot puree into the whipped cream. To serve, simply spoon the fool on top of the sliced peaches.